Pieces of mereology

Logic and Logical Philosophy 14 (2):211-234 (2005)
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Abstract

In this paper† we will treat mereology as a theory of some structures that are not axiomatizable in an elementary langauge and we will use a variable rangingover the power set of the universe of the structure). A mereological structure is an ordered pair M = hM,⊑i, where M is a non-empty set and ⊑is a binary relation in M, i.e., ⊑ is a subset of M × M. The relation ⊑ isa relation of being a mereological part . We formulate an axiomatization of mereological structures, different from Tarski’s axiomatization aspresented in [10] . We prove that these axiomatizations are equivalent . Of course, these axiomatizations are definitionally equivalent to thevery first axiomatization of mereology from [5], where the relation of being aproper part ⊏ is a primitive one.Moreover, we will show that Simons’ “Classical Extensional Mereology”from [9] is essentially weaker than Leśniewski’s mereology

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Andrzej Pietruszczak
Nicolaus Copernicus University

References found in this work

The Structure of Appearance.Nelson Goodman - 1956 - Studia Logica 4:255-261.
The calculus of individuals and its uses.Henry S. Leonard & Nelson Goodman - 1940 - Journal of Symbolic Logic 5 (2):45-55.
The Calculus of Individuals and Its Uses.Henry S. Leonard & Nelson Goodman - 1940 - Journal of Symbolic Logic 5 (3):113-114.
The Structure of Appearance.Paul Henle - 1952 - Journal of Symbolic Logic 17 (2):130-133.
Some complete calculi of individuals.Rolf A. Eberle - 1967 - Notre Dame Journal of Formal Logic 8 (4):267-278.

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